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Block #2,004,277

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/1/2017, 1:33:26 PM Β· Difficulty 10.7280 Β· 4,806,135 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
4b9289080e66100713f06bbcb4e1dc8e4713dbfbbe017f47c123d06113a41be4
View on Chainz β†—

Height

#2,004,277

Difficulty

10.728047

Transactions

2

Size

1.14 KB

Version

2

Bits

0aba614b

Nonce

800,107,574

Timestamp

3/1/2017, 1:33:26 PM

Confirmations

4,806,135

Mined by

⛏️ P2SHAW3cvehxZUA2aJc7pP5AcQHYKm2wGyF5u7

Merkle Root

67f10f546cc17961df1b821c79ebee1b07860a1db9a4c8cf9122d647680c7f3f
Transactions (2)
Coinbase472539f54237e9…d8fae341efe1ef
1 in β†’ 1 out8.6900 XPM110 B
AW3cvehx…2wGyF5u7
b64b489074ae71…2d8b4eb6e77604
6 in β†’ 2 out17.7875 XPM965 B
AVGCCq8K…7pwFqr1rAbfHPQRP…cc1QCTYa
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.898 Γ— 10⁹⁢(97-digit number)
88987326960868170818…60210627919039733759
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
8.898 Γ— 10⁹⁢(97-digit number)
88987326960868170818…60210627919039733759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.779 Γ— 10⁹⁷(98-digit number)
17797465392173634163…20421255838079467519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.559 Γ— 10⁹⁷(98-digit number)
35594930784347268327…40842511676158935039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.118 Γ— 10⁹⁷(98-digit number)
71189861568694536654…81685023352317870079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.423 Γ— 10⁹⁸(99-digit number)
14237972313738907330…63370046704635740159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.847 Γ— 10⁹⁸(99-digit number)
28475944627477814661…26740093409271480319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.695 Γ— 10⁹⁸(99-digit number)
56951889254955629323…53480186818542960639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.139 Γ— 10⁹⁹(100-digit number)
11390377850991125864…06960373637085921279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.278 Γ— 10⁹⁹(100-digit number)
22780755701982251729…13920747274171842559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.556 Γ— 10⁹⁹(100-digit number)
45561511403964503458…27841494548343685119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,727,376 XPMΒ·at block #6,810,411 Β· updates every 60s
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